Graph symmetry

Description

The last decade has seen parallel developments in computer science and combinatorics, both dealing with networks having strong symmetry properties. Both developments are centred on Cayley graphs: in the design of large interconnection networks, Cayley graphs arise as one of the most frequently used models; on the mathematical side, they play a central role as the prototypes of vertex-transitive graphs. The surveys published here provide an account of these developments, with a strong emphasis on the fruitful interplay of methods from group theory and graph theory that characterises the subject. Topics covered include: combinatorial properties of various hierarchical families of Cayley graphs (fault tolerance, diameter, routing, forwarding indices, etc.); Laplace eigenvalues of graphs and their relations to forwarding problems, isoperimetric properties, partition problems, and random walks on graphs; vertex-transitive graphs of small orders and of orders having few prime factors; distance transitive graphs; isomorphism problems for Cayley graphs of cyclic groups; infinite vertex-transitive graphs (the random graph and generalisations, actions of the automorphisms on ray ends, relations to the growth rate of the graph).

Subjects

Series Statement

• NATO ASI series. Series C, Mathematical and physical sciences ;

Other Editions

• Graph symmetry: algebraic methods and applicationsKluwer Academic Publishers1997-01-01
• Graph SymmetrypaperbackSpringer Netherlands2010-12-03
• Graph SymmetrySpringer2013-01-01